Highly selective Backlog Qs for JEE MainMathematicsCircle
A line is drawn through a fixed point P( , ) to cut the circle x²+y²=r² at A and B . Then P A P B is equal to
Options
- A( + )²-r²
- B²+ ²-r²
- C( - )²+r²
- DNone of the above
Correct answer
B. ²+ ²-r²
Step-by-step solution
The equation of any line through the point P( , ) is x- = y- =k (say) Any point on this line is ( +k , +k ) This point lies on the given circle, if ( +k )²+( +k )²=r² or k²+2 k( + ) + ²+ ²-r²=0 Which being quadratic in k , gives two values of k . Let P A=k₁, P B=k₂ , where k₁, k₂ are the roots of Eq. (i), then P A P B=k₁ k₂= ²+ ²-r²